Intersection of conjugate solvable subgroups in symmetric groups

Abstract

It is shown that for a solvable subgroup $G$ of an almost simple group $S$ which socle is isomorphic to $A_n$ $(n\ge 5)$ there are $x,y,z,t\in S$ such that $G\cap G^x\cap G^y\cap G^z\cap G^t=1.$